Scientists, engineers, developers, and artists employ various scanners and/or imagers to analyze, acquire, or reconstruct virtual representations of surfaces of tangible or physical objects. In practice, scanners detect only a finite subset of the surface of objects. As such, scanners typically provide a discretized model of the object. For instance, three-dimensional (3D) scanners and imagers acquire a discretized “point cloud” of data. The point cloud includes a finite set of spatial coordinates, each of which corresponds to a unique physical location on the various surfaces of the scanned object. To provide practical visualization, manipulation, or further analysis of the object, each of the various surfaces must be reconstructed from the discretized point cloud, e.g. a continuous 3D surface of the object must be inferred between the points of the point cloud.
Many of the currently available methods for reconstructing surfaces fail to reconstruct surfaces of thin objects (e.g., thin regions or structures of an object). For instance, some conventional methods include generating a mathematical model from the point cloud, where, at a particular point, the sign (i.e. whether a value of the model that is associated with the particular point is positive or negative) of the model indicates whether the particular point is within or outside of the model. These methods may fail when the sign of the model oscillates over a small region of space.